Collaborative Research: Construction and Analysis of Numerical Methods for Stochastic Inverse Problems with Application to Coastal Hydrodynamics

合作研究：随机反问题数值方法的构建和分析及其在海岸流体动力学中的应用

基本信息

批准号：
1818941
负责人：
Troy Butler
金额：
$ 17.5万
依托单位：
University of Colorado at Denver-Downtown Campus
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818941&HistoricalAwards=false
关键词：
Collaborative Research Construction Analysis Numerical

项目摘要

As observed in past hurricanes such as Katrina (2005), Ike (2008), Sandy (2012), and the sequence of hurricanes over the 2017 season, flooding due to storm surge and rainfall causes tremendous damage to coastal communities. Preparing for future hurricane impacts requires the ability to predict characteristics of inland flooding due to surge, most importantly water levels, currents, and extent of inundation. Accurate predictions of surge require determining critical inputs to models related to the physical characteristics of coastal regions that are expensive to obtain and evolve in time. This research project focuses on quantifying and reducing uncertainties in these critical inputs using novel mathematical techniques to both extract information from existing data and aid in the design of future data collection efforts.More specifically, this project focuses on the construction, analysis, and implementation of numerical methods for a stochastic inverse problem defined by the melding of observational data and high-fidelity mathematical models to perform scientific and engineering inference and prediction for complex physical systems. This research applies broadly to complex, time-evolving physical systems depending on high dimensional parameter spaces. Mathematical areas utilized in this research include computational measure theory, differential geometry, functional analysis, probability theory, and numerical analysis. Dissemination of results to the broader scientific community will be accomplished in part by the development and implementation of computational algorithms in public domain code that are applied to a state-of-the-art storm surge model.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

正如在过去的飓风中观察到的那样，例如卡特里娜（Katrina，2005），艾克（2008），桑迪（2012）以及2017赛季的飓风序列，由于风暴潮和降雨造成了巨大的破坏，对沿海社区造成了巨大破坏。为未来的飓风影响做准备，需要能够预测由于激增而引起的内陆洪水特征，最重要的是水位，水流和淹没程度。对激增的准确预测需要确定与沿海地区相关的物理特征相关的模型的关键输入，这些模型及时地获得和发展。该研究项目的重点是使用新型数学技术量化这些关键输入中的不确定性，从现有数据中提取信息，并有助于设计未来数据收集工作的设计。更具体地说，该项目侧重于构建，分析和实施数值方法，以实现在物理和高素质数学中定义的范围内的物理性和高素质数学的范围，以实现构建的方法，并将其实施系统。这项研究广泛地适用于复杂的，随时间变化的物理系统，具体取决于高维参数空间。本研究中使用的数学领域包括计算测量理论，差异几何，功能分析，概率理论和数值分析。将结果传播给更广泛的科学界将部分通过用于公共领域代码中计算算法的开发和实施，这些算法应用于最先进的风暴激增模型。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力和更广泛影响的评估来评估的支持。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Lp CONVERGENCE OF APPROXIMATE MAPS AND PROBABILITY DENSITIES FOR FORWARD AND INVERSE PROBLEMS IN UNCERTAINTY QUANTIFICATION

不确定性量化中正逆问题的近似映射和概率密度的Lp收敛性

DOI：
10.1615/int.j.uncertaintyquantification.2022038086
发表时间：
2022
期刊：
International Journal for Uncertainty Quantification
影响因子：
1.7
作者：
Butler, Troy;Wildey, Timothy;Zhang, W.
通讯作者：
Zhang, W.

Optimal experimental design for prediction based on push-forward probability measures

基于前推概率测度的预测优化实验设计

DOI：
10.1016/j.jcp.2020.109518
发表时间：
2020
期刊：
Journal of Computational Physics
影响因子：
4.1
作者：
Butler, T.;Jakeman, J.D.;Wildey, T.
通讯作者：
Wildey, T.

Enhancing piecewise‐defined surrogate response surfaces with adjoints on sets of unstructured samples to solve stochastic inverse problems

通过非结构化样本集上的伴随物增强分段定义的替代响应面，以解决随机逆问题

DOI：
10.1002/nme.6078
发表时间：
2019
期刊：
International Journal for Numerical Methods in Engineering
影响因子：
2.9
作者：
Mattis, Steven A.;Butler, Troy
通讯作者：
Butler, Troy

What do we hear from a drum? A data-consistent approach to quantifying irreducible uncertainty on model inputs by extracting information from correlated model output data

DOI：
10.1016/j.cma.2020.113228
发表时间：
2020-10
期刊：
Computer Methods in Applied Mechanics and Engineering
影响因子：
7.2
作者：
T. Butler;H. Hakula
通讯作者：
T. Butler;H. Hakula

Parameter estimation with maximal updated densities

使用最大更新密度的参数估计

DOI：
10.1016/j.cma.2023.115906
发表时间：
2023
期刊：
Computer Methods in Applied Mechanics and Engineering
影响因子：
7.2
作者：
Pilosov, Michael;del-Castillo-Negrete, Carlos;Yen, Tian Yu;Butler, Troy;Dawson, Clint
通讯作者：
Dawson, Clint